About Gears

• A wheel having teeth of uniform formation provided
on its circumferential surface.
• Gears are used to transmit motion at a definite and
constant velocity ratio in situations where the distance
b/w the axes of driver & driven shaft is short.
• The larger gear is called the gear the smaller, the
pinion.

In comparison with belt and chain drives, gear drive
is:
• More Compact
• Positive (without any slipping)
• Can operate at high speed
• Transmission of high power
Gears are manufactured by casting, machining,
stamping. Out of all method of production of gear by
machining is mostly used.

Classification of Gears
According to the position of axes of the shafts
 Parallel (Gears which connect parallel shafts)
 Intersecting ( would intersect at some angle)
 Non-intersecting and Non-parallel
(Gears which connect non parallel and non intersecting shafts )
1.Spur Gear 2.Helical Gear
3.Herringbone Gear 4.Rack and Pinion
Bevel Gear with straight, screw, spiral teeth's
worm and worm gears

According to the velocity of the gears
According to the type of gearing
According to the position of tooth on the gear surface
Low velocity less than 3 m/s
Medium velocity in b/w 3 – 15 m/s
High velocity more than 15 m/s
External gearing externally meshing
Internal gearing mesh internally, annular
wheel
Rack &pinion straight line gear-rack
circular wheel - pinion
A) Straight B) Inclined C) Curved

• The worm gearing is essentially a form of spiral
gearing in which the shafts are usually at right angles.
• When equal bevel gears (having equal teeth) connect
two shafts whose axes are mutually perpendicular,
then the bevel gears are known as mitres.

SPUR GEAR
 Teeth is parallel to axis of shaft
 Transmit power from one shaft to another parallel shaft
 Used in Electric screwdriver, oscillating sprinkler, windup
alarm clock, washing machine and clothes dryer

EXTERNAL SPUR GEARINTERNAL SPUR GEAR

HELICAL GEAR
 The teeth on helical gears are cut at an angle to the face of the
gear
 This gradual engagement makes helical gears operate much
more smoothly and quietly than spur gears
 One interesting thing about helical gears is that if the angles of
the gear teeth are correct, they can be mounted on
perpendicular shafts, adjusting the rotation angle by 90
degrees.
 Helical Gear is used in Automobile gear box because it
produces less noise than spur gear

HERRINGBONE GEAR
(double helical gears)
 To avoid axial thrust, two
helical gears of opposite
hand can be mounted side
by side, to cancel resulting
thrust forces
 Herringbone gears are
mostly used on heavy
machinery.

RACK AND PINION GEARS
Rack and pinion gears are used to convert rotation
(From the pinion) into linear motion (of the rack)
A perfect example of this is the steering system on
many cars

BEVEL GEARS
 Bevel gears are useful when the direction of a shaft's rotation
needs to be changed
 They are usually mounted on shafts that are 90 degrees apart,
but can be designed to work at other angles as well
 The teeth on bevel gears can be straight, spiral or hypoid
 locomotives, marine applications, automobiles, printing presses,
cooling towers, power plants, steel plants, railway track
inspection machines, etc.

Straight, spiral and hypoid bevel gears

WORM AND WORM GEAR
A worm drive is a cylindrical gear with a shallow
spiral thread that engages the worm gear in a non
intersecting, perpendicular axes configuration.
Worm gears are used when large gear reductions are
needed. It is common for worm gears to have
reductions of 20:1, and even up to 300:1 or greater
The worm can easily turn the gear, but the gear cannot
turn the worm
Worm gears are used widely in material handling and
transportation machinery, machine tools, automobiles
etc

 One of the newest designs for differentials is called the Torsen
differential. It uses a combination of worms and worm gears
that make each wheel independent of the other wheels. These
differentials are found in Hummers, large earth-moving
vehicles and some off-road vehicles.

Spur gear
ADVANTAGES DISADVANTAGES
• Spur gears have high power
transmission efficiency
• They are compact and easy
to install.
• Unlike belt drives, spur gear
drives have no Slip.
• They can be used to transmit
large amount of power (of
the order of 50,000 kW)
• Spur gear drives are costly
when compared to belt drives
• Spur gears produce a lot of
noise when operating at high
speeds.
• They cannot be used for long
distance power transmission.

Helical gear
• Helical gears are much less
noisy.
• They can handle more load
then a spur gear of
equivalent width and tooth
size.
• They can be made to
engage at angles.
• Efficiency is lost as the
angle becomes greater.
• Helical gears have a higher
load capacity but are
expensive to manufacture.
• They have an axial thrust,
This can however be
overcome by the use of
double helical gears by
having teeth with a 'v'
shape.

Bevel gears
• This gear makes it possible to
change the operating angle.
• Differing of the number of teeth
(effectively diameter) on each
wheel allows mechanical
advantage to be changed. By
increasing or decreasing the
ratio of teeth between the drive
and driven wheels one may
change the ratio of rotations
between the two, meaning that
the rotational drive and torque
of the second wheel can be
changed
• One wheel of such gear is
designed to work with its
complementary wheel and no
other.
• The shafts' bearings must be
capable of supporting
significant forces
• Must be precisely mounted.

Worm gear
• Worm gear drives operate
silently and smoothly.
• They occupy less space.
• They have good meshing
effectiveness.
• They can be used for
reducing speed and
increasing torque.
• Worm gear materials are
expensive.
• Worm drives have high
power losses and low
transmission efficiency.
• They produce a lot of heat,
due to resistance between
them.

NOMENCLATURE OF GEARS
1. Pitch circle It is an imaginary circle on which the teeth of the
mating gears are meshed.
2. Pitch circle
diameter(PCD)
It is the diameter of the pitch circle. The size of
the gear is usually specified by the pitch circle
diameter.
3. Diameteral pitch
(Pd)
It is the ratio of number of teeth to the pitch circle
diameter in millimetres.
It is denoted by Pd= T /D
4. Circular pitch It is the arc distance measured on the
circumference of the pitch circle from a point of
one tooth to the corresponding point on the next
tooth. Pc = π* D/T = π*m
5. Module It is the ratio of the pitch circle diameter in mm to
the number of teeth (indicates how big or small a
gear is), m = 1/Pd =D/T= Pc /π

6. Common
tangent
It is a common tangent at pitch circle of two mating
gears at the pitch points
7. Tooth face It is the surface of the gear tooth above the pitch
circle.
8. Tooth flank It is the surface of the gear tooth below the pitch
circle.
9. Crest of tooth It is the outside surface of tooth i.e. top surface.
10. Root of tooth It is the junction of tooth with material at the
bottom of tooth space.
11. Tooth
thickness
It is the thickness of the tooth measured along the
pitch circle
Tooth thickness= Pc /2 = 0.5Pc

14. Addendum
circle
It is the circle drawn through the top of the teeth
and is concentric with the pitch circle.
15. Dedendum
circle
It is the circle drawn through the bottom of the
teeth.
16. line of action it is the common tangent to the two base circles
that passes through the pitch point of two mating
gears
17. Base circle It is the circle from which the involute profile is
generated.
18. Clearance The difference between the dedendum of one gear
and the addendum of the mating gear
12. Addendum It is the radial distance of a tooth from the pitch
circle to the top of the tooth.
13. Dedendum It is the radial distance of a tooth from the pitch
circle to the bottom of the tooth.

 PRESSURE ANGLE OR ANGLE OF
OBLIQUITY
• It is the angle between the line of action and common tangent
through pitch point.
• It is the angle that determines the direction of pressure b/w the
mating teeth.
• It is also defines the shape of involute teeth and size of base
circle.
• The pressure angle is generally taken as14.5 or 20 deg.
• The larger pressure angles are advantageous as they give
strong tooth form with less under cutting.
• Higher pressure angle requires wide base and stronger teeth.

The relationship between radii of base (rb) and pitch circles (r)
and the pressure angle (ø ) is:
Base circle
Common tangent

 BACKLASH IN GEARS
• Backlash in gears is purposefully created to avoid jamming of
gear teeth.
• This is one of the design considerations of gears.
• The space between teeth must be made larger than the thickness
of tooth, both measured on the pitch circle. Otherwise, the gears
could mesh with jamming.
• The difference between tooth-space (Ts) and tooth thickness (Tt),
both measured on the pitch circle is known as backlash.
• In many applications such as instruments, differential gear trains
and servo-mechanisms require complete elimination of backlash
for proper functioning.
Linear back Lash = (Ts-Tb)

 CONTACT RATIO
• Contact ratio of gears is one of the important design aspects of spur
gear.
• This is a number, which indicates the average number of pairs of
teeth in contact.
• This is the ratio equal to the length of path of contact on pitch circle
divided by the circular pitch.
• Gears are generally designed to have a contact ratio larger than 1.2,
because any inaccuracies in mounting the gears might
--reduce the contact ratio
--increasing the possibility of impact between the meshing teeth
--consequently the noise level.
CONTACT RATIO =
length of path of contact
circular pitch

TEETH PROFILES
1. CYCLOIDAL TEETH
 Epicycloid
 Hypocycloid
2. INVOLUTE TEETH.

 CYCLOIDAL TEETH
• A cycloid is the curve traced by a point on the
circumference of a circle which rolls without slipping
on a fixed straight line.
• When a circle rolls without slipping on the outside of
a fixed (pitch) circle, the curve traced by a point on
the circumference of a circle is known as epicycloid.
• if a circle rolls without slipping on the inside of a
fixed (pitch) circle, then the curve traced by a point
on the circumference of a circle is called
hypocycloid.

 INVOLUTE TEETH
• An involute of a circle is a plane curve generated by a point on
a tangent, which rolls on the circle without slipping or by a
point on a taut string which is unwrapped from a reel
• In connection with toothed wheels, the circle is known as base
circle (generating profile by unwrapping string on this circle ).
 Conditions:
1. When base circle is in b/w addendum and dedendum circle, in
this case interference occurs because b/w base circle &
dedendum another curve is required..
2. When base circle is below dedendum circle then no
interference occurs because involute curve is from base circle
to addendum circle.

• The radius of curvature of involute varies continuously.
• It is zero at point 'a', (on the cylinder) and maximum at point
'c'(far away from the cylinder).
xby = line of action

Involute cycloidal
1. Single curvature
----Involute curve b/w base and
addendum circle
1. Double curvature
---epicycloid and hypocycloid
2. Constant pressure angle
---smooth running
2. Pressure angle varies
---less smooth running
3. Centre distance of involute gear
can be varied within limits
without changing the velocity ratio.
3. To be kept constant to keep
velocity ratio constant
4. Manufacturing easy (simple profile) 4. not easy

5. Interference problem
---only when Base circle is above
than dedendum
5. No interference problem
6. More wear of tooth surface 6. Less wear as convex face
engages with concave flank.

 INTERFERENCE IN GEARS
A little consideration will show, that if the radius of the addendum
circle of pinion is increased to O1N, the point of contact L will
move from L to N. When this radius is further increased, the point
of contact L will be on the inside of base circle of wheel and not on
the involute profile of tooth on wheel.
The tip of tooth on the pinion will then undercut the tooth on the
wheel at the root and remove part of the involute profile of tooth on
the wheel. This effect is known as interference and occurs when
the teeth are being cut.
The phenomenon when the tip of a tooth undercuts the root on
its mating gear is known as interference.

Minimum Number of Teeth on the Pinion in Order to Avoid
Interference

 ELIMINATION OF INTERFERENCE
• Use of a larger pressure angle can eliminate interference.
---The advantages of 20° pressure angle system are:
(i) Stronger tooth with higher load carrying capacity
(ii) Greater length of contact
• Interference can be eliminated by under-cutting of tooth.
• Elimination of interference is possible by tooth stubbing.
• Increasing the number of teeth on the gear can also eliminate
the chances of interference.
---The min. no. of teeth to avoid interference is :
• Increasing slightly the centre distance between the meshing
gears would also eliminate interference.

When two or more gears are made to mesh with
each other to transmit power from one shaft to
another, such a combination is called ‘gear train
or train of toothed wheels’.

Advantages
1. It transmits exact velocity ratio.
2. It may be used to transmit large power.
3. It may be used for small centre distances of shafts.
4. It has high efficiency.
5. It has reliable service.
6. It has compact layout.
Disadvantages
1. Since the manufacture of gears require special tools and equipment,
therefore it is costlier than other drives.
2. The error in cutting teeth may cause vibrations and noise during
operation.
3. It requires suitable lubricant and reliable method of applying it, for
the proper operation of gear drives.

Types of gear trains
1. Simple gear train
2. Compound gear train
3. Reverted gear train
4. Epicyclic gear train

 Simple gear train
• When there is only one gear on
each shaft as shown in fig, it is
known as simple gear train.
• When the distance between two
shafts is small, the two gears 1
and 2 are made to mesh with
each other to transmit motion
from one shaft to other as shown
in fig.
• Since the gear 1 drives 2,
therefore gear 1 is called the
driver and the gear 2 is called
the driven or follower.

 Since the speed ratio of gear train is the ratio of the speed of
the driver to the speed of the driven or follower and the ratio of
speeds of any pair of gears in mesh is the inverse of their
number of teeth, therefore
 It may be noted that ratio of the speed of the driven to the
speed of the driver is known as train value of the gear train.
Mathematically,
=Speed ratio =
=Train value
(Gear ratio)
=
teeth

 Sometimes, the distance between the two gears is large. The
motion from one gear to another, in such a case, may be
transmitted by either of the following two methods :
1. By providing the large sized gear, or
2. By providing one or more intermediate gears.
 It may be noted that when the number of intermediate gears
odd, the motion of both gears is like but if the number of
intermediate gears even, the motion of both gears is unlike.
 It is seen that the speed ratio and the train value of gears, is
independent of the size and the number of intermediate gears.

 These intermediate gears are called idler gears, as they do not
effect the speed ratio or train value of the system.
 The idler gears are used for the following two purposes :
1. To connect gears where a large distance is required, and
2. To obtain the desired direction of motion of the driven
gear(i.e. clockwise or anticlockwise).

 Compound gear train
• When there are more than one
gear on a shaft as shown in fig., it
is known as compound gear train.
• Compound gear trains are useful
in bridging over the space
between the driver and the driven.
• In this case, each intermediate
shaft has two gears rigidly fixed
to it so they may have the same
speed.

• Whenever the distance between the driver and the driven has
to be bridged over by intermediate gears and at the same time
a great speed ratio is required, then the advantage of
intermediate gears is intensified by providing compound gears
on intermediate shafts.
• One of these two gears mashes with the driver and the other
with the driven attached to the next shaft as shown in fig.

• Speed ratio of compound gear train is given by,
• Train value of compound gear train is given by,
• The advantage of compound train over a simple train is that a
much longer speed reduction from one shaft to the last shaft
can be obtained with small gears.
Speed ratio
Train value

 Reverted gear train
 When the axes of the first gear and
the last gear are co-axial, then the
gear train is known as reverted gear
train
 Here the gear 1 drives the gear 2 in
the opposite direction.
 Since the gear 2 and 3 form a
compound gear and the gear 3 will
rotate in the same direction as of gear
2.
 the gear 3 will drive the gear 4 in the
same direction as of gear 1.
 hence the motion of the first gear and
the last gear is like.

Let T1=number teeth on gear 1,
r1=pitch circle radius of gear 1, and
N1=speed of gear 1 in r.p.m.
Similarly,
T2, T3, T4= number of teeth on respective gears,
r2, r3, r4= pitch circle radius of respective gears, and
N2, N3, N4= speed of respective gears in r.p.m.
• Since the distance between the centers of the shafts of gears 1
and 2 as well as gears 3 and 4 is same, therefore
r1+r2 = r3+r4
• Also the pitch of the gears assumed to be the same, therefore
number of teeth on each gear is directly proportional to its
circumference or radius.
T1+T2 = T3+T4
And
Speed ratio

 Epicyclic gear train
 In an epicyclic gear train, the axis
of the shafts, over which the gears
are mounted, may move relative to
a fixed axis.
 When a gear 1 and arm 3 and gear
2 and arm 3 have a common axis.
 If the arm is fixed, the gear train is
simple and gear 1 can drive gear 2
or vice-versa, but if gear 1 is fixed
and the arm is rotated about the axis
then the gear 2 is forced to rotate
upon and around the gear 1.
 Such a motion is called epicyclic.

Compound epicylic gear train-sun and planet gear

Epicylic gear train with bevel gears :
Humpage’s speed reduction gear. Differential gear of an
automobile.

2014
By
GAURAV KUMAR
Thank you.

About Gears

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